a proprioceptive discussion on mechanism used for knee joint from 2000-2012: a literature review

8/10/2019 A Proprioceptive Discussion on Mechanism Used for Knee Joint from 2000-2012: A Literature Review

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International Journal of Scientific and Research Publications, Volume 4, Issue 5, May 2014 1ISSN 2250-3153

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A Proprioceptive Discussion on Mechanism Used for

Knee Joint from 2000-2012: A Literature Review

Prashant Choudhary*, Pawan Mishra

**, Vinayak Ranjan Dwivedi

***

*Department of Mechanical Engineering, Krishna Engineering College** Department of Mechanical Engineering, Krishna Engineering College

*** Department of Mechanical Engineering, ISM, Dhanbad

Abstract - A variety of active above knee prosthesis have been

manufactured over the past decade and there has been ambiguity

over the advantages and disadvantages of the various

counterparts.

The most Therefore, this study involves analysis and

comparison of various prosthesis based on the mechanism

employed.

I ndex Terms - Mechanism, Above-knee, Prosthesis, Trans-

femoral, Four-bar, Six bar, spherical;

I.

I NTRODUCTION

oss of limb has been a problem as long important part of an

above knee prosthesis is the mechanism employed for

satisfactory flexion and extension functions of the knee joint. as

man has been in existence. The earliest report regarding the

prosthetic usage returns to the time of Rig-Veda period, which is

between 3500- 1800 BC. [1,2]Ever since the beginning of

humanity, man has been using wooden cane as a support for

walking. Later this was replaced by roughly crafted peg legs and

hooks. With technological advances during the world wars, this

field saw major leap and first real prosthesis based on SolidAnkle Cushioned Heel was developed by J E Hanger.

A type of surgical operation that severs thigh section between

the knee and joint is known as Above Knee Amputation. It

generally happens when the amputee has gone through some

disease or some accident. The foot and shank sections are

completely lost post amputation while the thigh section is

partially lost. The purpose of this study is to review current

information regarding current prosthetic designs which can

emulate the unharmed limb with varying degrees.

II.

TYPES OF MECHANISMS EMPLOYED IN ABOVE

KNEE PROSTHESIS

The function of the knee mechanism is to exercise control

over absorption of motion of a knee in a prosthesis. This is

achieved in devices either by mechanical friction, or by

resistance offered to fluid flow. The swing control component of

a knee mechanism therefore is the mechanical control to dampen

the swing of the knee at the extremes of flexion and extension

Over the last decade the various mechanisms employed in above

knee prosthesis are 4-bar mechanisms,6-bar mechanisms and

Spherical mechanisms which exercise control over various

angles of flexion and extension.

The four bar linkage is of three types ,namely : the four bar

linkage with elevated instantaneous centre, the hyper-stabilized

four bar knee mechanism and the voluntary control four bar

mechanism. The elevated instantaneous centre provides for

stability at heel contact while the hyper-stabilized knee is more

of a locked knee mechanism which provides alignment stability

for less active amputees. The voluntary control four bar

mechanism provides stability at heel contact as well as heel push

off as it provides more control and is preferred by aggressivelyactive amputees.[3]

Six-bar mechanisms have been successfully used in some

knee joints by the Otto Bock Company. Also a few articles on

kinematic as well as design and performance of the six-bar

mechanism have also been published till date. Van de Veen

outlined the general constitution of multiple-bar linkage for the

prosthetic knee. A particular six-bar knee-ankle mechanism to

provide coordinate motion between knee and ankle joint during

walking and squatting was also designed by Patil and

Chakravorty. The six-bar mechanisms have much more design

variables as compared to four bar mechanisms. Therefore, six-bar

mechanisms can provide more functional advantages based on

appropriate design.[4]Despite its simple structure, the spherical mechanism

represents knee motion with good accuracy. With respect to the

previous more complex mechanism, though the results o

replication of natural motion were less satisfactory but are

counterbalanced by a reduction of computational costs, by an

improvement in numerical stability of the mathematical model

and by a reduction of the overall mechanical complexity of the

mechanism.[5]

III.

CONSTITUTION AND DESIGN OF MECHANISMS

A. FOUR BAR MECHANISMS:

The above-knee prosthesis as shown in figure 1 has a four- bar linkage arrangement at the knee by which the motion can be

transmitted from the thigh to foot during squatting action and

during the swing phase of walking. The four-bar linkage is

formed by four-bar link 1,2 3,and 4 with a short posterior link 2

designed after several trials, such that it creates an instantaneous

center which is located well above a corresponding single axis

knee center and posterior to the hip ankle line in full extension

This results in stability of the prosthesis during stance phase

Initiation of and moving of the Instantaneous center rapidly

down to the natural position of the anatomical knee joint can be

L

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done with a little effort of the hip muscles. Up to 10° of knee

flexion, the center of rotation is well above the location of a

single axis knee joint, which helps the amputee in being able to

control both extension and flexion voluntarily over this critical

range of motion. With this linkage arrangement a flexion angle

of 150° can be achieved, this enables the amputee to squat and

kneel comfortably. [3,6]

Fig. 1 A typical four bar mechanism

B. SIX BAR MECHANISMS:

Fundamental types of six-bar mechanisms are the Watt type

and Stephenson type as shown in figure 2.The particular

objective of design parameters is to constitute the six-bar knee

mechanism so that the shank is fixed to link 5 or 6 while the

thigh is fixed to link 1. Otherwise, if the shank is connected to

link 3, then the function of the six-bar knee mechanism will be

the same as that of four-bar mechanisms.

Fig.2. (a)Watt type six bar mechanism

2. (b) Stephenson type six bar mechanism

Based on these two types, the knee joint has four

configurations as shown in figure 3 :

Fig. 3 Configurations of six bar mechanism

KINEMATIC DESIGN OF SIX BAR MECHANISMS:

Considering the following six bar mechanism:

Fig. 5 A six bar mechanism

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The geometric center of the knee mechanism can be

calculated by the equations

7

17

1

i

i gc x x

7

17

1

i

i gc y y

where gc x and gc y

are the coordinates of the geometric

center of the knee mechanism and i x and i y

are are the

coordinates of the seven joints of the mechanism. After the

optimization method of Complex Penalty Function is applied, the

design parameters are obtained as [4,7] :

X T T

l l l x x x ,......,,......, ,14211621

=[25,71.6,40,37.9,28,21.8,31.7,19,17,35,32,383,14,26.7,88 ,11 ]

Then the six-bar knee mechanism can be designed, and the

trajectory generated by the mechanism is shown below :

Fig. 6 Trajectory generated by six bar mechanisms

C. SPHERICAL MECHANISM:

5-5 PARELLEL MECHANISM

A 5-5 model of the human knee which reproduces the passive

flexion of this prosthesis was discovered in the past. It has

proved to be particularly effective and provides a good

simulation of the passive motion compared to other models of the

knee and its implementation is very simple for optimization.

Fig. 7 A 5-5 Parallel mechanism

The geometry of the 5-5 mechanism is shown in figure 7. The

relative positions of the ligament insertions from total extension

to maximum flexion were analysed and for each ligament the

pair of points (one on the femur and the other on the tibia) which

showed the minimum change in distance were chosen. The three

points on the t ibia (A1, A2 and A3) and those corresponding onthe femur (B1, B2 and B3) are the centers of the spherical pairs

on three of the five legs of the equivalent mechanism. The four

condyles were then replaced by four best fitting spheres whose

centers (A4, A5 on the tibia and B4, B5 on the femur) are also

the centers of the two remaining legs. The length i L of each leg

is the distance between the spherical pairs on each link at the

initial position (full extension).

The closure equations of the mechanism constrain each pair

of points Ai – Bi to keep the same distance at each imposed

flexion angle:

22

ii P-B·R -A i L (where i=1,2,3....so on)

where points Ai and Bi are expressed in St and in Sf

respectively,.

is the2

L -norm of the vector,R the 3x3 rotation

matrix for the transformation of vector components from Sf to St

and P the position of the origin of Sf in St. Matrix R can be

expressed as function of three rotation parameters , and

:

R =

where c and s indicate the cosine and sine of the angle in

subscript and , and

represent the flexion, ab/adduction

and intra/extra rotation angles of the femur relatively to the tibia

Expression (2) can be applied for right legs. If knee flexion is

fixed, the five equations of system (1) depend only on five

unknowns, i.e. the three components of vector P and the angles

and

only.[21,22,23,24,25,28,34,37,40,41]

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1-DEGREE OF FREEDOM (DOF) SPHERICAL MECHANISM:

A 1-Dof spherical mechanism is shown figure 8:

Fig. 8 1-Degree of freedom (Dof) spherical mechanism

The closure equations for design in this case is given below :

2

i

2

iiLP-B·R -A

(where i=1,2)

and0P-B·R -A 33

where R and P have the same values as above.[5,16,17,18,26,27]

IV.

STABILITY OF DIFFERENT MECHANISMS

A. Four bar mechanism :

The stability diagram of the various types of four bar

mechanisms are given in figure 9,figure 10 and figure 11. .The

four bar mechanism with raised instantaneous centre has been

designed to give extreme stability at heel contact by having the

instantaneous centre for full extension of the knee located

considerably posterior to the load line at heel contact. The

physical arrangement of a hyper-stabilized knee is often similar

to the four bar mechanism with elevated instantaneous centre but

it has very positive alignment stability built in to it. The

voluntary control four bar knee is designed not only to giveamputee ability to control knee stability at both heel contact and

push-off, but to have complete control of knee stability over a

limited range of knee flexion.[3,6,12,13]

Fig. 10 Stability diagram of a 4 bar mechanism with raised instantaneous centre

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Fig. 11 stability diagram of a hyper-stabilized 4 bar mechanism

Fig. 12 stability diagram of voluntary control 4 bar mechanism

B. SIX BAR MECHANISM:

If two links connected by a revolute joint in a six bar

kinematic chain, they have the same angular velocity at the same

instant and position, which means that the links have no relative

motion between them , the joint is referred to as Instant Inactive

Joint. For example, if the 4-bar kinematic chain, shown in figure

13 (a), is in such a position that links 3 and 4 are collinear and

links 1 and 2 have the same angular velocity, then the revolute

joint A is an Instant inactive joint in this position. For a self

locking mechanism, the Instant inactive joint (IIJ) must exist. In

figure 13(b), if link 1 (or 2) is fixed, link 2 (or 1) cannot drive the

mechanism no matter how large the driving moment is

Obviously, the more IIJ exists, the more stable the mechanism is

In the four-bar kinematic chain, only one IIJ can exist. However

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depending on the design, the six-bar kinematic chain can have as

many as four Instant inactive joints exists.[4,14,15,30,32]

Fig. 13 Instant inactive joints in six bar mechanisms

C. SPHERICAL MECHANISM:

The numerical stability of spherical mechanism is

quantitatively analysed starting from geometrical optimization.

Optimized parameters are collected in a relevant vector s, having

35 or 16 components, depending on the model. For each vector s,3000 error vectors s are randomly generated whose

components are chosen all inside the interval [-1; + 1]. Thus, for

each optimized mechanism, 3000 modified geometries are

defined by s s sm

. The joint motion of each modified

mechanism is compared with that of the relevant original optimal

computing the mean squared and weighted error merr .This error

is an index of the sensitivity of each identified model to

geometric parameter variation. Moreover, the number of

singularity problems met during this procedure is counted,in

order to quantify the tendency of a model to generate

singularities. [5,9,10,18,20,29,31,32,38]

V.

COMPARISON BETWEEN 4 BAR, SIX BAR AND

SPHERICAL MECHANISMS

Mechanism Advantages Disadvantages

4-bar

Stable centre of

rotation.

Anterior weight

bearing axis.

Ease of slopeand stair

descent.

Higher cost.

6-bar

High Stability.

Kinematic

Stability on

terrains and

speed ranges.

More weight.

Asymmetric gait

pattern.

Spherical

Lower

mechanical

complexity .

Light weight.

Replication of

natural motion

is less

satisfactory.

VI.

CONCLUSIONThe kinematic performance of the several different

mechanisms such as four-bar linkage and six-bar linkage are

shown in above figures. In this paper are compared with pure

motion without reference to the masses or forces involved in it

The comparison of the trajectory of the joint in swing phase of

the six-bar linkage knee with that of a four-bar knee mechanism

shows that six-bar linkage knee has better performance than four-

bar knee mechanism. Also the comparison between various six

bar mechanism shows that the performance of six bar mechanism

is better than other mechanisms.

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AUTHORS

First Author – Pawan Mishra, Assistant Professor, Krishna

Engineering College, [email protected]

Second Author –

Prashant Choudhary, Student,KrishnaEngineering College, [email protected]

Third Author – Anuj sharma, Student,Krishna Engineering

College, [email protected]

Correspondence Author – Pawan Mishra, Assistant Professor,

Krishna Engineering College, [email protected]

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a proprioceptive discussion on mechanism used for knee joint from 2000-2012: a literature review

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